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Adaptively controlling and minimizing regret in unknown dynamical systemswhile controlling the growth of the system state is crucial in real-worldapplications. In this work, we study the problem of stabilization and regretminimization of linear over-actuated dynamical systems. We propose anoptimism-based algorithm that leverages possibility of switching betweenactuating modes in order to alleviate state explosion during initial timesteps. We theoretically study the rate at which our algorithm learns astabilizing controller and prove that it achieves a regret upper bound of$\mathcal{O}(\sqrt{T})$.

Joint Stabilization and Regret Minimization through Switching in Over-Actuated Systems (extended version)